Mmm..... Aura's are of the person, not the persons gender. And even then, you can't tell what a person is like from their aura. Basically, the aura, is a feeling that someone sensitive to it, can use to distinguish who the person is. I.E. A dog can tell who "Mark" and "George" are, just by smell. The same can be done by people.
Basically, the Aura is more or less a feeling of someone.
Some people whom are socially withdrawn, can feel when someone is around, these people also become sensitive to other feelings and in most cases, can feel who it is that is around.
I would not say that it is magic, or psychic or something as far fetched as that. I would say it is more or less a detection of body heat, or a slight heat change, or even acute pheromone and body smell detection.
Basically, no one can physically, or "spiritually" tell if you are male or female transgender. So basically, the best way to Prove it, is to prove how much happier you are, being yourself in front of them, or in public.
